[backport 2.3.x] BUG(string dtype): groupby/resampler.min/max returns float on all NA strings (#60985)

pandas/core/groupby/groupby.py

@@ -85,6 +85,7 @@ class providing the base-class of operations.
     is_numeric_dtype,
     is_object_dtype,
     is_scalar,
+    is_string_dtype,
     needs_i8_conversion,
     pandas_dtype,
 )
@@ -1945,8 +1946,13 @@ def _agg_py_fallback(
             # preserve the kind of exception that raised
             raise type(err)(msg) from err
 
-        if ser.dtype == object:
+        dtype = ser.dtype
+        if dtype == object:
             res_values = res_values.astype(object, copy=False)
+        elif is_string_dtype(dtype):
+            # mypy doesn't infer dtype is an ExtensionDtype
+            string_array_cls = dtype.construct_array_type()  # type: ignore[union-attr]
+            res_values = string_array_cls._from_sequence(res_values, dtype=dtype)
 
         # If we are DataFrameGroupBy and went through a SeriesGroupByPath
         # then we need to reshape

pandas/tests/groupby/test_reductions.py

@@ -20,6 +20,7 @@
     isna,
 )
 import pandas._testing as tm
+from pandas.tests.groupby import get_groupby_method_args
 from pandas.util import _test_decorators as td
 
 
@@ -710,6 +711,93 @@ def test_min_empty_string_dtype(func, string_dtype_no_object):
     tm.assert_frame_equal(result, expected)
 
 
+@pytest.mark.parametrize("min_count", [0, 1])
+@pytest.mark.parametrize("test_series", [True, False])
+def test_string_dtype_all_na(
+    string_dtype_no_object, reduction_func, min_count, test_series
+):
+    # https://github.com/pandas-dev/pandas/issues/60985
+    if reduction_func == "corrwith":
+        # corrwith is deprecated.
+        return
+
+    dtype = string_dtype_no_object
+
+    if reduction_func in [
+        "any",
+        "all",
+        "idxmin",
+        "idxmax",
+        "mean",
+        "median",
+        "std",
+        "var",
+    ]:
+        kwargs = {}
+    elif reduction_func in ["kurt"]:
+        kwargs = {"min_count": min_count}
+    elif reduction_func in ["count", "nunique", "quantile", "sem", "size"]:
+        kwargs = {}
+    else:
+        kwargs = {"min_count": min_count}
+
+    expected_dtype, expected_value = dtype, pd.NA
+    if reduction_func in ["all", "any"]:
+        expected_dtype = "bool"
+        # TODO: For skipna=False, bool(pd.NA) raises; should groupby?
+        expected_value = False if reduction_func == "any" else True
+    elif reduction_func in ["count", "nunique", "size"]:
+        # TODO: Should be more consistent - return Int64 when dtype.na_value is pd.NA?
+        if (
+            test_series
+            and reduction_func == "size"
+            and dtype.storage == "pyarrow"
+            and dtype.na_value is pd.NA
+        ):
+            expected_dtype = "Int64"
+        else:
+            expected_dtype = "int64"
+        expected_value = 1 if reduction_func == "size" else 0
+    elif reduction_func in ["idxmin", "idxmax"]:
+        expected_dtype, expected_value = "float64", np.nan
+    elif min_count > 0:
+        expected_value = pd.NA
+    elif reduction_func == "sum":
+        # https://github.com/pandas-dev/pandas/pull/60936
+        expected_value = ""
+
+    df = DataFrame({"a": ["x"], "b": [pd.NA]}, dtype=dtype)
+    obj = df["b"] if test_series else df
+    args = get_groupby_method_args(reduction_func, obj)
+    gb = obj.groupby(df["a"])
+    method = getattr(gb, reduction_func)
+
+    if reduction_func in [
+        "mean",
+        "median",
+        "kurt",
+        "prod",
+        "quantile",
+        "sem",
+        "skew",
+        "std",
+        "var",
+    ]:
+        msg = f"dtype '{dtype}' does not support operation '{reduction_func}'"
+        with pytest.raises(TypeError, match=msg):
+            method(*args, **kwargs)
+        return
+
+    result = method(*args, **kwargs)
+    index = pd.Index(["x"], name="a", dtype=dtype)
+    if test_series or reduction_func == "size":
+        name = None if not test_series and reduction_func == "size" else "b"
+        expected = Series(expected_value, index=index, dtype=expected_dtype, name=name)
+    else:
+        expected = DataFrame({"b": expected_value}, index=index, dtype=expected_dtype)
+    tm.assert_equal(result, expected)
+
+
 @pytest.mark.parametrize("min_count", [0, 1])
 def test_string_dtype_empty_sum(string_dtype_no_object, min_count):
     # https://github.com/pandas-dev/pandas/issues/60229